Behavior of Multiple Supported Secondary System Mounted on a Torsionally Coupled Primary System

Dynamic behavior of a multiple supported secondary system mounted on a torsionally coupled primary system is presented for bi-directional random ground excitation, which is idealized as a broad band stationary random process. Response behavior of the multiple supported secondary system is investigated by considering and ignoring the interaction between the primary and the secondary systems. The response quantities of interest are the standard deviation of the absolute acceleration at a specified node and the bending moment at a specified support of the multiple supported secondary system. For the no interaction case, input to the support of the secondary system is prescribed in the form of both pseudo and cross power spectral density function (PSDF), characterizing the correlation between various supports of the multiple supported secondary system. For the interaction case, the conventional ground PSDF can directly be used as input to the combined structural system. The responses are obtained by the frequency domain spectral analysis. The responses are obtained under a number of important parametric variations. Numerical results of the study show that the responses decrease with the increase in the mass ratio between the secondary and the primary system. Under the tuned condition, a definite maxima is observed for the higher mass ratio. For strong and weak torsionally coupled primary systems under the tuned and interaction conditions the normalized acceleration show a definite minima when orientation of the secondary system is 45° with the major axes of the primary system. For the other cases, the response quantities show a definite maxima at this orientation.